Home
Class 12
MATHS
Evaluate: int(-pi/2)^(pi/2)log((a-s inth...

Evaluate: `int_(-pi/2)^(pi/2)log((a-s intheta)/(a+sintheta))dtheta,a >0`

Text Solution

Verified by Experts

`f(theta)=log((a-sintheta)/(a+sin theta))`
`:.f(-theta)=log((a+sin theta)/(a-sin theta))`
`=-log((a-sin theta)/(a+sin theta))`
`=-f(theta)`
Hence the integrand is anodd function.
So, the given integral is zero.
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.1|4 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.2|17 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_((-pi)/2)^(pi/2)cosxdx .

Evaluate: int_(-pi//2)^(pi//2)xsin dx

Evaluate : int_((-pi)/2)^(pi/2)xcosxdx .

Evaluate int_(0)^(pi/2)logsinxdx

Evaluate: int_(0)^(pi/2)(costheta)/((1+sintheta)(2+sintheta))d theta .

Evaluate int_(0)^(pi//2)(costheta)/((1+sintheta)(2+sintheta))d theta

Evaluate: int_(-pi)^(3pi)log(s e ctheta-t a ntheta)dtheta

Evaluate: int_(-pi/2)^(2pi)sin^(-1)(sinx)dx

Evaluate: int_(pi//4)^(pi//4)log(sinx+cosx)dx

Evaluate: int_0^(pi/2)[cost]dt

CENGAGE-DEFINITE INTEGRATION -JEE Advanced Previous Year
  1. Evaluate: int(-pi/2)^(pi/2)log((a-s intheta)/(a+sintheta))dtheta,a >0

    Text Solution

    |

  2. Solve: (x+2)^3=2x(x^2-1)

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. Find the roots of the following quadratic equations x^2-2x-3

    Text Solution

    |

  6. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  7. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  8. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Find A × B, A × A and B × A : A = {1, 2, 3} and B = {1, −4}.

    Text Solution

    |

  11. Evaluate: int(-pi//2)^(pi//2)(cosx)/(1+e^x)dx

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  15. For a in R (the set of all real numbers), a!=-1), (lim)(nvecoo)((1^a...

    Text Solution

    |

  16. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

    Text Solution

    |

  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  18. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  19. Given A = {2,4,5 }, B = {2, 5}, C = {3, 4} and D = {1, 3, 5}, check if...

    Text Solution

    |

  20. ("lim")(xvecoo)((n^2)/(n^2))^(n(n-1)i se q u a lto e (b) e^2 (c) e^(...

    Text Solution

    |

  21. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |